Material

Abstracts and Presentations

If you would like a copy of any of the technical program presentations, please contact guillaume.ginolhac@univ-smb.fr.

Below are summaries of some of the presentations.

Lectures

## 1

Title: How to improve accelerated optimization algorithms by embedding information about objective into the design

Speaker: Vorobyov Sergiy

Abstract: 

Accelerated optimization algorithms are designed to exploit the available information about the objective or to optimize the worst case performance of an algorithm based on the available information. Several acceleration mechanisms have been developed. The acceleration mechanism based on the so-called estimating sequences is very flexible and allows for applications beyond the basic accelerated first-order optimization algorithms design in the so-called black-box scenario. Fast algorithms specialized for a problem at hand are also popular for solving particular problems of high practical importance. In the black box framework, we first present a new accelerated gradient-based method for solving smooth unconstrained optimization problems. The new method exploits additional information about the objective function and is built by embedding a heavy-ball type of momentum into the Fast Gradient Method (FGM). We devise a generalization of the estimating sequences, which allows for encoding any form of information about the objective function that can aid in further accelerating the minimization process. In the black box framework, we propose a construction for the generalized estimating sequences, which is obtained by exploiting the history of the previously constructed estimating functions. Moreover, we prove better bound for the number iterations required to find a point with a given tolerance. We procced than by presenting a new class of generalized composite estimating sequences for composite non-smooth objectives, devised by exploiting the information contained in the iterates that are formed during the minimization process. We present a new accelerated first-order methods for minimizing convex functions with composite objective structure. The proposed method is equipped with backtracking line-search, and exhibits an accelerated convergence rate independent of whether the true value of the Lipschitz constant is known. Moreover, the method is also robust to the inexact knowledge of the strong convexity parameter. The efficiency of our proposed methods together with their robustness properties will also be shown by extensive numerical evaluations on both synthetic and real-world datasets.

Short Talks

Title: Gradient Estimation for Structured Reinforcement Learning 

Speaker: Matthieu Jonckheere

Abstract: 

Many Markov decision processes (MDPs) have large state and action spaces as well as non-convex objective functions, which hinders the convergence properties of many reinforcement learning (RL) algorithms. We show that these difficulties can be circumvented by exploiting some simple structure of the underlying MDP. We focus on a particular class of RL algorithms, called policy-gradient methods, which directly optimize the policy parameter via stochastic gradient ascent, without necessarily relying on value-function estimation. These methods are known to perform better on MDPs with large state and action spaces, but they sometimes experience slow convergence due to the high variance of the gradient estimator.

We design a new family of gradient estimators, called score-aware gradient estimators (SAGEs), that apply to policy parameterizations under which the stationary distribution of the MDP forms an exponential family parameterized by the policy parameter. Our second contribution is a convergence result showing that, under appropriate assumptions, the policy under SAGE-based policy-gradient methods has a large probability of converging to an optimal policy, provided that it starts sufficiently close. This holds also when the objective function is nonconvex and has multiple optimal policies. Lastly, we compare numerically the performance of a SAGE-based policy gradient method with that of actor-critic, a classical policy-gradient method.

This is joint work with Céline Comte (LAAS CNRS), Jaron Sanders (Eindhoven University of Technology) and Albert Senen-Cerda (LAAS, CNRS).

Title:  On Modified Cramér-Rao Bounds 

Speaker: Sara El-Bouch

Abstract: 

In this talk, I will first introduce the Modified Cramér-Rao Bound (MCRB) for non-standard estimation problems. I will exhibit the link between the Modified Cramér-Rao bound, a ubiquitous bound in non-standard estimation problems, and the Hybrid Cramér-Rao bound, under a mild constraint. Leveraging this link enables us to derive a recursive estimation scheme of the MCRB (under constraint) for Markovian Dynamic Systems. Finally, I will discuss the extension of the Modified Cramér-Rao bound to matrix Lie groups.

Title:  Non-parametric Online Change Point Detection on Riemannian Manifolds

Speaker: Xiuheng Wang 

Abstract: 

Non-parametric detection of change points in streaming time series data that belong to Euclidean spaces has been extensively studied in the literature. Nevertheless, when the data belongs to a Riemannian manifold, existing approaches are no longer applicable as they fail to account for the structure and geometry of the manifold. In this presentation, we introduce a non-parametric algorithm for online change point detection in manifold-valued data streams. This algorithm monitors the generalized Karcher mean of the data, computed using stochastic Riemannian optimization. We provide theoretical bounds on the detection and false alarm rate performances of the algorithm, using a new result on the non-asymptotic convergence of the stochastic Riemannian gradient descent. We apply our algorithm to two different Riemannian manifolds. Experimental results with both synthetic and real data illustrate the performance of the proposed method. 

Title:  Kalman filter for dynamic source power estimation based on empirical covariances

Speaker: Cyril Cano

Abstract: 

Traditional Kalman filters are not immediately suitable for the estimation of source power with sample covariance matrices as observations. This comes from the fact that the observations must be expressed as a linear function of the source power. The objective of this work is to formalize such a filter, in particular by enabling the calculation of both the mean and covariance of the observation model noise, which is here correlated with the state vector. The proposed method is evaluated on simulated data representative of a dynamic radio astronomy framework.